Comparing clustered sampling designs for spatially explicit estimation of population density

Spatially explicit capture-recapture methods do not assume that animals have equal access to sampling devices (e.g., detectors), which allows for gaps in the sampling extent and nonuniform (e.g., clustered) sampling designs. However, the performance (i.e., relative root mean squared error [RRMSE], confidence interval coverage, relative bias and relative standard error) of clustered detector arrays has not been thoroughly evaluated. I used simulations to evaluate the performance of various detector and cluster spacings, cluster configurations (i.e., number of detectors arranged in a square grid), sampling extents and number of sampling occasions for estimating population density, the relationship between detection rate and distance to a detector from the animal's center of activity (sigma) and base detection rates, using American black bears (Ursus americanus) as a case study. My simulations indicated that a wide range of detector configurations can provide reliable estimates if spacing between detectors in clusters is 1 sigma and 3 sigma. A number of cluster configurations and occasion lengths produced estimates that were unbiased, resulted in good spatial coverage, and were relatively precise. Moreover, increasing the duration of sampling, establishing large study areas, increasing detection rates and spacing clusters so that cross-cluster sampling of individuals can occur could help ameliorate deficiencies in the detector layout. These results have application for a wide array of species and sampling methods (e.g., DNA sampling, camera trapping, mark-resight and search-encounter) and suggest that clustered sampling can significantly reduce the effort necessary to provide reliable estimates of population density across large spatial extents that previously would have been infeasible with nonclustered sampling designs.